MinT - Best Known (88−65, 88, s)-Nets in Base 32

Best Known (88−65, 88, s)-Nets in Base 32

(88−65, 88, 120)-Net over F₃₂ — Constructive and digital

Digital (23, 88, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 88, 120)-net over F₃₂, using
- net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
    - a function field by SÃ©mirat [i]

(88−65, 88, 177)-Net in Base 32 — Constructive

(23, 88, 177)-net in base 32, using

8 times m-reduction [i] based on (23, 96, 177)-net in base 32, using
- base change [i] based on digital (7, 80, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(88−65, 88, 185)-Net over F₃₂ — Digital

Digital (23, 88, 185)-net over F₃₂, using

t-expansion [i] based on digital (21, 88, 185)-net over F₃₂, using
- net from sequence [i] based on digital (21, 184)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 21 and N(F) ≥ 185, using
    - a curve from the manYPoints database [i]

(88−65, 88, 5084)-Net in Base 32 — Upper bound on s

There is no (23, 88, 5085)-net in base 32, because

1 times m-reduction [i] would yield (23, 87, 5085)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 89082 271254 602368 033446 183432 792022 234646 471769 859212 568883 277140 303160 693944 501628 931725 450026 988036 359779 555713 381802 924849 463110 > 32⁸⁷ [i]